Quantum gases in rotating optical lattices

The thesis is structured into two main parts so as to cover bosons and fermions in rotating optical lattices separately. In the first part, after a brief introduction to ultracold atoms in optical lattices, we review the single-particle physics for the lowest (s) band of a periodic potential under an artificial magnetic field created by rotation. Next, we discuss rotational effects on the first excited (p) band of the lattice, extending the methods available for the lowest band. We conclude the first part with a discussion of many-body physics in rotating lattice systems using a mean-field approach and investigate how the transition boundary between superfluid and Mott insulator phases is affected by the single-particle spectrum. In this context, we also examine a possible coexistent phase of Mott insulator and bosonic fractional quantum Hall states, appearing for certain system parameters near the Mott insulator lobes in the phase diagram. The second part starts with the proposal of a realization and detection scheme for the so-called topological Hofstadter insulator, which basically reveals the single-particle spectrum discussed before. The scheme depends on a measurement of the density profile for noninteracting fermions in a rotating optical lattice with a superimposed harmonic trapping potential. This method also allows one to measure the quantized Hall conductance, a feature which appears when the Fermi energy lies in an energy gap of the lattice potential. Finally, we explore the Bardeen-Cooper-Schrieffer type of pairing of fermionic atoms in optical lattices under an artificial magnetic field by paying special attention to single-particle degeneracies and present our results for the vortex lattice structure of the paired fermionic superfluid phase.